Nowadays, the most used method in studies of the coevolution of hosts and symbionts is phylogenetic tree reconciliation. A crucial issue in this method is that from a biological point of view, reasonable cost values for an event-based parsimonious reconciliation are not easily chosen. Different approaches have been developed to infer such cost values for a given pair of host and symbiont trees. However, a major limitation of these approaches is their inability to model the invasion of different host species by a same symbiont species (referred to as a spread event), which is thought to happen in symbiotic relations. To mention one example, the same species of insects may pollinate different species of plants. This results in multiple associations observed between the symbionts and their hosts (meaning that a symbiont is no longer specific to a host), that are not compatible with the current methods of coevolution. In this paper, we propose a method, called AmoCoala (a more realistic version of a previous tool called Coala) which for a given pair of host and symbiont trees, estimates the probabilities of the cophylogeny events, in presence of spread events, relying on an approximate Bayesian computation (ABC) approach. The algorithm that we propose, by including spread events, enables the multiple associations to be taken into account in a more accurate way, inducing more confidence in the estimated sets of costs and thus in the reconciliation of a given pair of host and symbiont trees. Its rooting in the tool Coala allows it to estimate the probabilities of the events even in the case of large datasets. We evaluate our method on synthetic and real datasets. The software is available at \url{https://team.inria.fr/erable/en/software/amocoala/}